Firstly, in [1]}, the convexity property of the level sets of a log-concave function plays a role in proving the Orlicz Pólya-Szegö principle. But for the general \(W_0^{1,\Phi }(G)\)  functions, the level sets of functions are sets more general than convex bodies. Thus, it is crucial to figure out the structure of the level sets of \(W_0^{1,\Phi }(G)\) . In this paper, we show that the level sets of \(W_0^{1,\Phi }(G)\)  functions are sets of finite perimeter and define the Steiner symmetrization of the level sets in a different way (see Section REF ), which makes it possible to make use of the functional Steiner symmetrization to prove the affine Orlicz Pólya-Szegö principle.
